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- Working with limits leads us directly into an important conversation around the topic of continuity. So were going to answer the question, when is a function continuous? Well, in order to determine when the function is or is not continuous, we need to know what continuous means. Ah, first kind of an informal definition, the idea of continuous means basically I can draw the graph without lifting my pencil. Its just a continuous curve without lifting the pencil for a gap or a jump or an asymptote, its just continuous. Now a more formal mathematical definition states that a continuous function will satisfy three conditions for all points. And well call those points a. The first condition is that f of a is defined. So the function cant be undefined at the given point. In addition, we need the limit as x approaches a of f of x to exist. So for example, if the function is approaching two different numbers from two different sides, the limit does not exist. But the all important one th
